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Exam 22: Gausss Law

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Question 1

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A spherical, non-conducting shell of inner radius r₁= 10 cm and outer radius r₂= 15 cm carries a total charge Q = 15 μC distributed uniformly throughout its volume. What is the electric field at a distance r= 12 cm from the center of the shell?

A) 5.75 × 10³ N/C
B) 0
C) 2.87 × 10⁶ N/C
D) 5.75 × 10⁶ N/C
E) 2.87 × 10³ N/C

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Question 2

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State Gauss's law.

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The total flux summed over any...

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Question 3

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A uniform electric field = E₀ is set-up in a region of space. A frame is placed in that region in such a way that its plane is perpendicular to the y-axis. Which of the following changes would decrease the magnitude of the electric flux through the frame?

The electric field in a region of space is oriented along the positive y axis. A circle of radius R is placed in the xz-plane. The flux of the electric field through this circle is Φ. The same electric field passing through a second circle of radius 2R parallel to xz-plane would result in a flux equal to

A region of space contains an electric field = E₁ + E₂ where E₁ and E₂ are positive constants. A frame whose corners are located at (x, y, z) = (a/2, 0, a/2), (-a/2, 0,-a/2), (a/2, 0,-a/2), and (-a/2, 0, a/2). What is the magnitude of the electric flux through the frame?

If a charge is located at the center of a spherical volume and the electric flux through the surface of the sphere is Φ₀, what is the flux through the surface if the radius of the sphere doubles?

A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r₁ = R/4 the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r₂ = 2R?

A point charge q = +1 μC is located at the origin. What is the flux of the electric field of this charge through a square whose corners are (x, y, z) = (1, 1, 1) , (-1, 1, 1) , (-1, 1, -1) , and (1, 1, -1) ?

Outside a spherically symmetric charge distribution of net charge Q, Gauss's law can be used to show that the electric field at a given distance

Gauss's law can be applied using any surface.

Gaussian surfaces A and B enclose the same positive charge +Q. The area of Gaussian surface A is three times larger than that of Gaussian surface B. The flux of electric field through Gaussian surface A is

A non-conducting sphere of radius R = 7 cm carries a charge Q = 4 mC distributed uniformly throughout its volume. At what distance, measured from the center of the sphere does the electric field reach a value equal to half its maximum value?

If the net flux through a closed surface is zero, then there can be no charge or charges within that surface.

If the electric flux through a circular area is 5.0 Nm²/C, what is the electric flux through a circle of double the diameter assuming the orientations of the circles are the same and the electric field is uniform?

A region of space contains a uniform electric field oriented along the y-axis. A frame of surface area A is placed perpendicular to the y-axis in the xz-plane. The magnitude of the electric flux through this frame is Φ₀. A second frame is placed in the same electric field in such a way that the magnitude of the electric flux through it is Φ₀/2. How is the plane of second frame oriented with respect to the plane of the first one?

A positive charge Q is located at the center of an imaginary Gaussian cube of sides a. The flux of the electric field through the surface of the cube is Φ. A second, negative charge -Q is placed next to Q inside the cube. Which of the following statements will be true in this case?

A long straight line of charge has a uniform positive charge per unit length λ. The line is partially enclosed in a long rectangular box of length L and ends of area A, the line running through the center of each end. The electric flux through the surface of the box is

An advantage in evaluating surface integrals related to Gauss's law for symmetric charge distributions is

An infinitely long cylinder of radius R = 2 cm carries a uniform charge density ρ = 18 μC/ m³. Calculate the electric field at distance r = 1 cm from the axis of the cylinder.

Three parallel flat planes of charge are separated by a distance d between each of the planes. The charge density on each of the planes is σ. The maximum magnitude of the electric field in the vicinity of the planes is